RNA folding: models and perspectives

Modeling Loop Composition and Ion Concentration Effects in RNA Hairpin Folding Stability

The ability to accurately predict RNA hairpin structure and stability for different loop sequences and salt conditions is important for understanding, modeling, and designing larger RNA folds. However, traditional RNA secondary structure models cannot treat loop-sequence and ionic effects on RNA hairpin folding. Here, we describe a general, three-dimensional (3D) conformation-based computational method for modeling salt concentration-dependent conformational distributions and the detailed 3D structures for a set of three RNA hairpins that contain a variable, 15-nucleotide loop sequence. For a given RNA sequence, the new, to our knowledge, method integrates a Vfold2D two-dimensional structure folding model with IsRNA coarse-grained molecular dynamics 3D folding simulations and Monte Carlo tightly bound ion estimations of ion-mediated electrostatic interactions. The model predicts free-energy landscapes for the different RNA hairpin-forming sequences with variable salt conditions. The theoretically predicted results agree with the experimental fluorescence measurements, validating the strategy. Furthermore, the theoretical model goes beyond the experimental results by enabling in-depth 3D structural analysis, revealing energetic mechanisms for the sequence- and salt-dependent folding stability. Although the computational framework presented here is developed for RNA hairpin systems, the general method may be applied to investigate other RNA systems, such as multiway junctions or pseudoknots in mixed metal ion solutions.

Investigations on the interface of nucleic acid aptamers and binding targets

Nucleic acid aptamers are single-stranded DNA or RNA of 20-100 nucleotides in length that have attracted substantial scientific interest due to their ability to specifically bind to target molecules via the formation of three-dimensional structures. Compared to traditional protein antibodies, aptamers have several advantages, such as their small size, high binding affinity, specificity, flexible structure, being chemical synthesizable and modifiable, good biocompatibility, high stability and low immunogenicity, which all contribute to their widely applications in the biomedical field. To date, much progress has been made in the study and applications of aptamers, however, detailed information on how aptamers bind to their targets is still scarce. Over the past few decades, many methods have been introduced to investigate the aptamer-target binding process, such as measuring the main kinetic or thermodynamic parameters, detecting the structural changes of the binding complexes, etc. Apart from traditional physicochemical methods, various types of molecular docking programs have been applied to simulate the aptamer-target interactions, while these simulations also have limitations. To facilitate the further research on the interactions, herein, we provide a brief review to illustrate the recent advances in the study of aptamer-target interactions. We summarize the binding targets of aptamers, such as small molecules, macromolecules, and even cells. Their binding constants (KD) are also summarized. Methods to probe the aptamer-target binding process, such as surface plasmon resonance (SPR), circular dichroism spectroscopy (CD), isothermal titration calorimetry (ITC), footprinting assay, truncation and mutation assay, nuclear magnetic resonance spectroscopy (NMR), X-ray crystallography and molecular docking simulation are indicated. The binding forces mediating the aptamer-target interactions, such as hydrogen bonding, electrostatic interaction, the hydrophobic effect, π-π stacking and van der Waals forces are summarized. The challenges and future perspectives are also discussed.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

A New Method to Predict Ion Effects in RNA Folding

The strong interaction between metal ions in solution and highly charged RNA molecules is critical for RNA structure formation and stabilization. Metal ions binding to RNA can induce RNA structural changes that are important for RNA cellular functions. Therefore, quantitative modeling of the ion effects is essential for RNA structure prediction and RNA-based molecular design. Recently, inspired by the increasing experimental evidence that supports the importance of ion correlation and fluctuation in ion-RNA interactions, we developed a new computational model, Monte Carlo Tightly Bound Ion (MCTBI) model. The validity of the model is shown by the improved accuracy in the predictions for ion binding properties and ion-dependent free energies for RNA structures. In this chapter, using homodimeric tetraloop-receptor docking as an illustrative example, we showcase the MCTBI method for the computational prediction of the ion effects in RNA folding.

Intrinsic Base-Pair Rearrangement in the Hairpin Ribozyme Directs RNA Conformational Sampling and Tertiary Interface Formation

Dynamic fluctuations in RNA structure enable conformational changes that are required for catalysis and recognition. In the hairpin ribozyme, the catalytically active structure is formed as an intricate tertiary interface between two RNA internal loops. Substantial alterations in the structure of each loop are observed upon interface formation, or docking. The very slow on-rate for this relatively tight interaction has led us to hypothesize a double conformational capture mechanism for RNA-RNA recognition. We used extensive molecular dynamics simulations to assess conformational sampling in the undocked form of the loop domain containing the scissile phosphate (loop A). We observed several major accessible conformations with distinctive patterns of hydrogen bonding and base stacking interactions in the active-site internal loop. Several important conformational features characteristic of the docked state were observed in well-populated substates, consistent with the kinetic sampling of docking-competent states by isolated loop A. Our observations suggest a hybrid or multistage binding mechanism, in which initial conformational selection of a docking-competent state is followed by induced-fit adjustment to an in-line, chemically reactive state only after formation of the initial complex with loop B.

Fluorescence-Based Strategies to Investigate the Structure and Dynamics of Aptamer-Ligand Complexes

In addition to the helical nature of double-stranded DNA and RNA, single-stranded oligonucleotides can arrange themselves into tridimensional structures containing loops, bulges, internal hairpins and many other motifs. This ability has been used for more than two decades to generate oligonucleotide sequences, so-called aptamers, that can recognize certain metabolites with high affinity and specificity. More recently, this library of artificially-generated nucleic acid aptamers has been expanded by the discovery that naturally occurring RNA sequences control bacterial gene expression in response to cellular concentration of a given metabolite. The application of fluorescence methods has been pivotal to characterize in detail the structure and dynamics of these aptamer-ligand complexes in solution. This is mostly due to the intrinsic high sensitivity of fluorescence methods and also to significant improvements in solid-phase synthesis, post-synthetic labeling strategies and optical instrumentation that took place during the last decade. In this work, we provide an overview of the most widely employed fluorescence methods to investigate aptamer structure and function by describing the use of aptamers labeled with a single dye in fluorescence quenching and anisotropy assays. The use of 2-aminopurine as a fluorescent analog of adenine to monitor local changes in structure and fluorescence resonance energy transfer (FRET) to follow long-range conformational changes is also covered in detail. The last part of the review is dedicated to the application of fluorescence techniques based on single-molecule microscopy, a technique that has revolutionized our understanding of nucleic acid structure and dynamics. We finally describe the advantages of monitoring ligand-binding and conformational changes, one molecule at a time, to decipher the complexity of regulatory aptamers and summarize the emerging folding and ligand-binding models arising from the application of these single-molecule FRET microscopy techniques.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

Exploring ion induced folding of a single-stranded DNA oligomer from molecular simulation studies

One crucial issue in DNA hydration is the effect of salts on its conformational features. This has relevance in biology as cations present in the cellular environment shield the negative charges on the DNA backbone, thereby reducing the repulsive force between them. By screening the negative charges along the backbone, cations stabilize the folded structure of DNA. To study the effect of the added salt on single-stranded DNA (ss-DNA) conformations, we have performed room temperature molecular dynamics simulations of an aqueous solution containing the ss-DNA dodecamer with the 5'-CGCGAATTCGCG-3' sequence in the presence of 0.2, 0.5, and 0.8 M NaCl. Our calculations reveal that in the presence of the salt, the DNA molecule forms more collapsed coil-like conformations due to the screening of negative charges along the backbone. Additionally, we demonstrated that the formation of an octahedral inner-sphere complex by the strongly bound ion plays an important role in the stabilization of such folded conformation of DNA. Importantly, it is found that ion-DNA interactions can also explain the formation of non-sequential base stackings with longer lifetimes. Such non-sequential base stackings further stabilize the collapsed coil-like folded form of the DNA oligomer.

Tetracycline determines the conformation of its aptamer at physiological magnesium concentrations

Synthetic riboswitches are versatile tools for the study and manipulation of biological systems. Yet, the underlying mechanisms governing its structural properties and regulation under physiological conditions are poorly studied. We performed spectroscopic and calorimetric experiments to explore the folding kinetics and thermodynamics of the tetracycline-binding aptamer, which can be employed as synthetic riboswitch, in the range of physiological magnesium concentrations. The dissociation constant of the ligand-aptamer complex was found to strongly depend on the magnesium concentration. At physiological magnesium concentrations, tetracycline induces a significant conformational shift from a compact, but heterogeneous intermediate state toward the completely formed set of tertiary interactions defining the regulation-competent structure. Thus, the switching functionality of the tetracycline-binding aptamer appears to include both a conformational rearrangement toward the regulation-competent structure and its thermodynamic stabilization.

Rapid RNA-ligand interaction analysis through high-information content conformational and stability landscapes

The structure and biological properties of RNAs are a function of changing cellular conditions, but comprehensive, simultaneous investigation of the effect of multiple interacting environmental variables is not easily achieved. We have developed an efficient, high-throughput method to characterize RNA structure and thermodynamic stability as a function of multiplexed solution conditions using Förster resonance energy transfer (FRET). In a single FRET experiment using conventional quantitative PCR instrumentation, 19,400 conditions of MgCl₂, ligand and temperature are analysed to generate detailed empirical conformational and stability landscapes of the cyclic diguanylate (c-di-GMP) riboswitch. The method allows rapid comparison of RNA structure modulation by cognate and non-cognate ligands. Landscape analysis reveals that kanamycin B stabilizes a non-native, idiosyncratic conformation of the riboswitch that inhibits c-di-GMP binding. This demonstrates that allosteric control of folding, rather than direct competition with cognate effectors, is a viable approach for pharmacologically targeting riboswitches and other structured RNA molecules.

The structure and biological properties of RNAs are a function of changing cellular conditions. Here, Baird et al. report a high-throughput Förster resonance energy transfer (FRET) method to rapidly compare RNA structure modulation by cognate and non-cognate ligands across multiplexed solution conditions.

Crystal structure of group II intron domain 1 reveals a template for RNA assembly

Although the importance of large noncoding RNAs is increasingly appreciated, our understanding of their structures and architectural dynamics remains limited. In particular, we know little about RNA folding intermediates and how they facilitate the productive assembly of RNA tertiary structures. Here, we report the crystal structure of an obligate intermediate that is required during the earliest stages of group II intron folding. Composed of domain 1 from the Oceanobacillus iheyensis group II intron (266 nucleotides), this intermediate retains native-like features but adopts a compact conformation in which the active site cleft is closed. Transition between this closed and the open (native) conformation is achieved through discrete rotations of hinge motifs in two regions of the molecule. The open state is then stabilized by sequential docking of downstream intron domains, suggesting a 'first come, first folded' strategy that may represent a generalizable pathway for assembly of large RNA and ribonucleoprotein structures.

RNA-Binding Efficacy of N-Phenylbenzohydroxamic Acid: An Invitro and Insilico Approach

RNA has attracted recent attention for its key role in gene expression and hence targeting by small molecules for therapeutic intervention. This study is aimed to elucidate the specificity of RNA binding affinity of parent compound of N-arylhydroxamic acids series, N-phenylbenzohydroxamic acid trivially named as PBHA,C6H5NOH.C6H5C˭O. The binding behavior was examined by various biophysical methods such as absorption, fluorescence, and viscosity measurements. Molecular docking was also done. The value of affinity constant and overall binding constant was calculated 5.79±0.03×10(4) M(-1) and K'=1.09±0.03×10(5) M(-1), respectively. The Stern-Volmer constant Ksv obtained was 2.28±0.04×10(4) M(-1). The compound (PBHA) shows a concentration-based enhancement of fluorescence intensity with increasing RNA concentration. Fluorescence quenching of PBHA-RNA complex in presence of K4 [Fe(CN)6] was also observed. Viscometric studies complimented the UV results where a continuous increase in relative viscosity of the RNA solution was observed with added optimal PBHA concentration. All the experimental evidences indicate that PBHA can strongly bind to RNA through an intercalative mode.

Using sm-FRET and denaturants to reveal folding landscapes

RNA folding studies aim to clarify the relationship among sequence, tridimensional structure, and biological function. In the last decade, the application of single-molecule fluorescence resonance energy transfer (sm-FRET) techniques to investigate RNA structure and folding has revealed the details of conformational changes and timescale of the process leading to the formation of biologically active RNA structures with subnanometer resolution on millisecond timescales. In this review, we initially summarize the first wave of single-molecule FRET-based RNA techniques that focused on analyzing the influence of mono- and divalent metal ions on RNA function, and how these studies have provided very valuable information about folding pathways and the presence of intermediate and low-populated states. Next, we describe a second generation of single-molecule techniques that combine sm-FRET with the use of chemical denaturants as an emerging powerful approach to reveal information about the dynamics and energetics of RNA folding that remains hidden using conventional sm-FRET approaches. The main advantages of using the competing interplay between folding agents such as metal ions and denaturants to observe and manipulate the dynamics of RNA folding and RNA-ligand interactions is discussed in the context of the adenine riboswitch aptamer.

Coarse-Grained HiRE-RNA Model for ab Initio RNA Folding beyond Simple Molecules, Including Noncanonical and Multiple Base Pairings

HiRE-RNA is a coarse-grained model for RNA structure prediction and the dynamical study of RNA folding. Using a reduced set of particles and detailed interactions accounting for base-pairing and stacking, we show that noncanonical and multiple base interactions are necessary to capture the full physical behavior of complex RNAs. In this paper, we give a full account of the model and present results on the folding, stability, and free energy surfaces of 16 systems with 12 to 76 nucleotides of increasingly complex architectures, ranging from monomers to dimers, using a total of 850 μs of simulation time.

HOTAIR forms an intricate and modular secondary structure

Long noncoding RNAs (lncRNAs) have recently emerged as key players in fundamental cellular processes and diseases, but their functions are poorly understood. HOTAIR is a 2,148-nt-long lncRNA molecule involved in physiological epidermal development and in pathogenic cancer progression, where it has been demonstrated to repress tumor and metastasis suppressor genes. To gain insights into the molecular mechanisms of HOTAIR, we purified it in a stable and homogenous form in vitro, and we determined its functional secondary structure through chemical probing and phylogenetic analysis. The HOTAIR structure reveals a degree of structural organization comparable to well-folded RNAs, like the group II intron, rRNA, or lncRNA steroid receptor activator. It is composed of four independently folding modules, two of which correspond to predicted protein-binding domains. Secondary structure elements that surround protein-binding motifs are evolutionarily conserved. Our work serves as a guide for "navigating" through the lncRNA HOTAIR and ultimately for understanding its function.

Fluorescence tools to investigate riboswitch structural dynamics

Riboswitches are novel regulatory elements that respond to cellular metabolites to control gene expression. They are constituted of highly conserved domains that have evolved to recognize specific metabolites. Such domains, so-called aptamers, are folded into intricate structures to enable metabolite recognition. Over the years, the development of ensemble and single-molecule fluorescence techniques has allowed to probe most of the mechanistic aspects of aptamer folding and ligand binding. In this review, we summarize the current fluorescence toolkit available to study riboswitch structural dynamics. We fist describe those methods based on fluorescent nucleotide analogues, mostly 2-aminopurine (2AP), to investigate short-range conformational changes, including some key steady-state and time-resolved examples that exemplify the versatility of fluorescent analogues as structural probes. The study of long-range structural changes by Förster resonance energy transfer (FRET) is mostly discussed in the context of single-molecule studies, including some recent developments based on the combination of single-molecule FRET techniques with controlled chemical denaturation methods. This article is part of a Special Issue entitled: Riboswitches.

Mapping RNA structure in vitro using nucleobase-specific probes

RNAs have to adopt specific three-dimensional structures to fulfill their biological functions. Therefore exploring RNA structure is of interest to understand RNA-dependent processes. Chemical probing in vitro is a very powerful tool to investigate RNA molecules under a variety of conditions. Among the most frequently used chemical reagents are the nucleobase-specific probes dimethyl sulfate (DMS), 1-cyclohexyl-3-(2-morpholinoethyl) carbodiimide metho-p-toluenesulfonate (CMCT) and β-ethoxy-α-ketobutyraldehyde (kethoxal). These chemical reagents modify nucleotides which are not involved in hydrogen bonding or protected by a ligand, such as proteins or metabolites. Upon performing modification reactions with all three chemicals the accessibility of all four nucleobases can be determined. With this fast and inexpensive method local changes in RNA secondary and tertiary structure, as well as the formation of contacts between RNA and its ligands can be detected independent of the RNA's length.

Single-molecule studies of riboswitch folding

The folding dynamics of riboswitches are central to their ability to modulate gene expression in response to environmental cues. In most cases, a structural competition between the formation of a ligand-binding aptamer and an expression platform (or some other competing off-state) determines the regulatory outcome. Here, we review single-molecule studies of riboswitch folding and function, predominantly carried out using single-molecule FRET or optical trapping approaches. Recent results have supplied new insights into riboswitch folding energy landscapes, the mechanisms of ligand binding, the roles played by divalent ions, the applicability of hierarchical folding models, and kinetic vs. thermodynamic control schemes. We anticipate that future work, based on improved data sets and potentially combining multiple experimental techniques, will enable the development of more complete models for complex RNA folding processes. This article is part of a Special Issue entitled: Riboswitches.

Advances in methods for native expression and purification of RNA for structural studies

Many RNAs present unique challenges in obtaining material suitable for structural or biophysical characterization. These issues include synthesis of chemically and conformationally homogeneous RNAs, refolding RNA purified using denaturing preparation techniques, and avoiding chemical damage. To address these challenges, new methodologies in RNA expression and purification have been developed seeking to emulate those commonly used for proteins. In this review, recent developments in the preparation of high-quality RNA for structural biology and biophysical applications are discussed, with an emphasis on native methods.

Structural dynamics of a mitochondrial tRNA possessing weak thermodynamic stability

Folding dynamics are ubiquitously involved in controlling the multivariate functions of RNAs. While the high thermodynamic stabilities of some RNAs favor purely native states at equilibrium, it is unclear whether weakly stable RNAs exist in random, partially folded states or sample well-defined, globally folded conformations. Using a folding assay that precisely tracks the formation of native aminoacylable tRNA, we show that the folding of a weakly stable human mitochondrial (hmt) leucine tRNA is hierarchical with a distinct kinetic folding intermediate. The stabilities of the native and intermediate conformers are separated by only about 1.2 kcal/mol, and the species are readily interconvertible. Comparison of folding dynamics between unmodified and fully modified tRNAs reveals that post-transcriptional modifications produce a more constrained native structure that does not sample intermediate conformations. These structural dynamics may thus be crucial for recognition by some modifying enzymes in vivo, especially those targeting the globular core region, by allowing access to pretransition state conformers. Reduced conformational sampling of the native, modified tRNAs could then permit improved performance in downstream processes of translation. More generally, weak stabilities of small RNAs that fold in the absence of chaperone proteins may facilitate conformational switching that is central to biological function.

Chemical probing of RNA in living cells

RNAs need to adopt a specific architecture to exert their task in cells. While significant progress has been made in describing RNA folding landscapes in vitro, understanding intracellular RNA structure formation is still in its infancy. This is in part due to the complex nature of the cellular environment but also to the limited availability of suitable methodologies. To assess the intracellular structure of large RNAs, we recently applied a chemical probing technique and a metal-induced cleavage assay in vivo. These methods are based on the fact that small molecules, like dimethyl sulfate (DMS), or metal ions, such as Pb(2+), penetrate and spread throughout the cell very fast. Hence, these chemicals are able to modify accessible RNA residues or to induce cleavage of the RNA strand in the vicinity of a metal ion in living cells. Mapping of these incidents allows inferring information on the intracellular conformation, metal ion binding sites or ligand-induced structural changes of the respective RNA molecule. Importantly, in vivo chemical probing can be easily adapted to study RNAs in different cell types.

On the importance of cotranscriptional RNA structure formation

The expression of genes, both coding and noncoding, can be significantly influenced by RNA structural features of their corresponding transcripts. There is by now mounting experimental and some theoretical evidence that structure formation in vivo starts during transcription and that this cotranscriptional folding determines the functional RNA structural features that are being formed. Several decades of research in bioinformatics have resulted in a wide range of computational methods for predicting RNA secondary structures. Almost all state-of-the-art methods in terms of prediction accuracy, however, completely ignore the process of structure formation and focus exclusively on the final RNA structure. This review hopes to bridge this gap. We summarize the existing evidence for cotranscriptional folding and then review the different, currently used strategies for RNA secondary-structure prediction. Finally, we propose a range of ideas on how state-of-the-art methods could be potentially improved by explicitly capturing the process of cotranscriptional structure formation.

Full design automation of multi-state RNA devices to program gene expression using energy-based optimization

Small RNAs (sRNAs) can operate as regulatory agents to control protein expression by interaction with the 5′ untranslated region of the mRNA. We have developed a physicochemical framework, relying on base pair interaction energies, to design multi-state sRNA devices by solving an optimization problem with an objective function accounting for the stability of the transition and final intermolecular states. Contrary to the analysis of the reaction kinetics of an ensemble of sRNAs, we solve the inverse problem of finding sequences satisfying targeted reactions. We show here that our objective function correlates well with measured riboregulatory activity of a set of mutants. This has enabled the application of the methodology for an extended design of RNA devices with specified behavior, assuming different molecular interaction models based on Watson-Crick interaction. We designed several YES, NOT, AND, and OR logic gates, including the design of combinatorial riboregulators. In sum, our de novo approach provides a new paradigm in synthetic biology to design molecular interaction mechanisms facilitating future high-throughput functional sRNA design.

Is our current knowledge of in vivo RNA-RNA interactions and thermodynamics enough to perform the unsupervised computational design of fully synthetic sequences encoding functional RNAs in living cells? Recent work gave a positive answer for the challenging problem of designing activating riboregulators. This was done by integrating theory and computation to develop a physicochemical framework for the design of regulatory RNA systems, using Watson-Crick interactions and optimization algorithms. Still, the objective function was not directly validated, preventing using with confidence the methodology for other systems. We here validate experimentally an objective function relying on free energies of RNA complex activation and formation, which allows extending the framework to produce logic devices that can be implemented to program gene expression. We demonstrate that it is possible to design increasingly sophisticated and modular functions, pointing our results out that energy-based optimization methods can perform the large combinatorial search required for RNA design.

Transient RNA structure features are evolutionarily conserved and can be computationally predicted

Functional RNA structures tend to be conserved during evolution. This finding is, for example, exploited by comparative methods for RNA secondary structure prediction that currently provide the state-of-art in terms of prediction accuracy. We here provide strong evidence that homologous RNA genes not only fold into similar final RNA structures, but that their folding pathways also share common transient structural features that have been evolutionarily conserved. For this, we compile and investigate a non-redundant data set of 32 sequences with known transient and final RNA secondary structures and devise a dedicated computational analysis pipeline.

Molecular dynamics simulation of RNA pseudoknot unfolding pathway

Many biological functions of RNA molecules are related to their pseudoknot structures. It is significant for predicting the structure and function of RNA that learning about the stability and the process of RNA pseudoknot folding and unfolding. The structural features of mouse mammary tumor virus (MMTV) RNA pseudoknot in different ion concentration, the unfolding process of the RNA pseudoknot, and the two hairpin helices that constitute the RNA pseudoknot were studied with all atom molecule dynamics simulation method in this paper. We found that the higher cation concentration can cause structure of the RNA molecules more stable, and ions played an indispensable role in keeping the structure of RNA molecules stable; the unfolding process of hairpin structure was corresponding to the antiprocess of its folding process. The main pathway of pseudoknot unfolding was that the inner base pair opened first, and then, the two helices, which formed the RNA pseudoknot opened decussately, while the folding pathway of the RNA pseudoknot was a helix folding after formation of the other helix. Therefore, the unfolding process of RNA pseudoknot is different from the antiprocess of its folding process, and the unfolding process of each helix in the RNA pseudoknot is similar to the hairpin structure’s unfolding process, which means that both are the unzipping process.

Single-molecule chemical denaturation of riboswitches

To date, single-molecule RNA science has been developed almost exclusively around the effect of metal ions as folding promoters and stabilizers of the RNA structure. Here, we introduce a novel strategy that combines single-molecule Förster resonance energy transfer (FRET) and chemical denaturation to observe and manipulate RNA dynamics. We demonstrate that the competing interplay between metal ions and denaturant agents provides a platform to extract information that otherwise will remain hidden with current methods. Using the adenine-sensing riboswitch aptamer as a model, we provide strong evidence for a rate-limiting folding step of the aptamer domain being modulated through ligand binding, a feature that is important for regulation of the controlled gene. In the absence of ligand, the rate-determining step is dominated by the formation of long-range key tertiary contacts between peripheral stem-loop elements. In contrast, when the adenine ligand interacts with partially folded messenger RNAs, the aptamer requires specifically bound Mg²⁺ ions, as those observed in the crystal structure, to progress further towards the native form. Moreover, despite that the ligand-free and ligand-bound states are indistinguishable by FRET, their different stability against urea-induced denaturation allowed us to discriminate them, even when they coexist within a single FRET trajectory; a feature not accessible by existing methods.

Ion-mediated RNA structural collapse: effect of spatial confinement

RNAs are negatively charged molecules that reside in cellular environments with macromolecular crowding. Macromolecular confinement can influence the ion effects in RNA folding. In this work, using the recently developed tightly bound ion model for ion fluctuation and correlation, we investigate the effect of confinement on ion-mediated RNA structural collapse for a simple model system. We find that for both Na(+) and Mg(2+), the ion efficiencies in mediating structural collapse/folding are significantly enhanced by the structural confinement. This enhancement of ion efficiency is attributed to the decreased electrostatic free-energy difference between the compact conformation ensemble and the (restricted) extended conformation ensemble due to the spatial restriction.

The structural stabilization of the κ three-way junction by Mg(II) represents the first step in the folding of a group II intron

Folding of group II introns is characterized by a first slow compaction of domain 1 (D1) followed by the rapid docking of other domains to this scaffold. D1 compaction initiates in a small subregion encompassing the κ and ζ elements. These two tertiary elements are also the major interaction sites with domain 5 to form the catalytic core. Here, we provide the first characterization of the structure adopted at an early folding step and show that the folding control element can be narrowed down to the three-way junction with the κ motif. In our nuclear magnetic resonance studies of this substructure derived from the yeast mitochondrial group II intron Sc.ai5γ, we show that a high affinity Mg(II) ion stabilizes the κ element and enables coaxial stacking between helices d′ and d′′, favoring a rigid duplex across the three-way junction. The κ-element folds into a stable GAAA-tetraloop motif and engages in A-minor interactions with helix d′. The addition of cobalt(III)hexammine reveals three distinct binding sites. The Mg(II)-promoted structural rearrangement and rigidification of the D1 core can be identified as the first micro-step of D1 folding.

Mss116p: a DEAD-box protein facilitates RNA folding

RNA folding is an essential aspect underlying RNA-mediated cellular processes. Many RNAs, including large, multi-domain ribozymes, are capable of folding to the native, functional state without assistance of a protein cofactor in vitro. In the cell, trans-acting factors, such as proteins, are however known to modulate the structure and thus the fate of an RNA. DEAD-box proteins, including Mss116p, were recently found to assist folding of group I and group II introns in vitro and in vivo. The underlying mechanism(s) have been studied extensively to explore the contribution of ATP hydrolysis and duplex unwinding in helicase-stimulated intron splicing. Here we summarize the ongoing efforts to understand the novel role of DEAD-box proteins in RNA folding.

RNA plasticity and selectivity applicable to therapeutics and novel biosensor development

Aptamers are short, single-stranded nucleic acid sequences that are selected in vitro from large oligonucleotide libraries based on their high affinity to a target molecule. Hence, aptamers can be thought of as a nucleic acid analog to antibodies. However, several viewpoints hold that the potential of aptamers arises from interesting characteristics that are distinct from, or in some cases, superior to those of antibodies. This review summarizes the recent achievements in aptamer programs developed in our laboratory against basic and therapeutic protein targets. Through these studies, we became aware of the remarkable conformational plasticity and selectivity of RNA, on which the published report has not shed much light even though this is evidently a crucial feature for the strong specificity and affinity of RNA aptamers.

Predicting ion-nucleic acid interactions by energy landscape-guided sampling

The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.

Thermodynamic origins of monovalent facilitated RNA folding

Cations have long been associated with formation of native RNA structure and are commonly thought to stabilize the formation of tertiary contacts by favorably interacting with the electrostatic potential of the RNA, giving rise to an "ion atmosphere". A significant amount of information regarding the thermodynamics of structural transitions in the presence of an ion atmosphere has accumulated and suggests stabilization is dominated by entropic terms. This work provides an analysis of how RNA-cation interactions affect the entropy and enthalpy associated with an RNA tertiary transition. Specifically, temperature-dependent single-molecule fluorescence resonance energy transfer studies have been exploited to determine the free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) of folding for an isolated tetraloop-receptor tertiary interaction as a function of Na(+) concentration. Somewhat unexpectedly, increasing the Na(+) concentration changes the folding enthalpy from a strongly exothermic process [e.g., ΔH° = -26(2) kcal/mol at 180 mM] to a weakly exothermic process [e.g., ΔH° = -4(1) kcal/mol at 630 mM]. As a direct corollary, it is the strong increase in folding entropy [Δ(ΔS°) > 0] that compensates for this loss of exothermicity for the achievement of more favorable folding [Δ(ΔG°) < 0] at higher Na(+) concentrations. In conjunction with corresponding measurements of the thermodynamics of the transition state barrier, these data provide a detailed description of the folding pathway associated with the GAAA tetraloop-receptor interaction as a function of Na(+) concentration. The results support a potentially universal mechanism for monovalent facilitated RNA folding, whereby an increasing monovalent concentration stabilizes tertiary structure by reducing the entropic penalty for folding.

Metal-ion-dependent folding of a uranyl-specific DNAzyme: insight into function from fluorescence resonance energy transfer studies

Fluorescence resonance energy transfer (FRET) has been used to study the global folding of an uranyl (UO(2)(2+))-specific 39E DNAzyme in the presence of Mg(2+), Zn(2+), Pb(2+), or UO(2)(2+). At pH 5.5 and physiological ionic strength (100 mM Na(+)), two of the three stems in this DNAzyme folded into a compact structure in the presence of Mg(2+) or Zn(2+). However, no folding occurred in the presence of Pb(2+) or UO(2)(2+); this is analogous to the "lock-and-key" catalysis mode first observed in the Pb(2+)-specific 8-17 DNAzyme. However, Mg(2+) and Zn(2+) exert different effects on the 8-17 and 39E DNAzymes. Whereas Mg(2+) or Zn(2+)-dependent folding promoted 8-17 DNAzyme activity, the 39E DNAzyme folding induced by Mg(2+) or Zn(2+) inhibited UO(2)(2+)-specific activity. Group IIA series of metal ions (Mg(2+), Ca(2+), Sr(2+)) also caused global folding of the 39E DNAzyme, for which the apparent binding affinity between these metal ions and the DNAzyme decreases as the ionic radius of the metal ions increases. Because the ionic radius of Sr(2+) (1.12 Å) is comparable to that of Pb(2+) (1.20 Å), but contrary to Pb(2+), Sr(2+) induces the DNAzyme to fold under identical conditions, ionic size alone cannot account for the unique folding behaviors induced by Pb(2+) and UO(2)(2+). Under low ionic strength (30 mM Na(+)), all four metal ions (Mg(2+), Zn(2+), Pb(2+), and UO(2)(2+)), caused 39E DNAzyme folding, suggesting that metal ions can neutralize the negative charge of DNA-backbone phosphates in addition to playing specific catalytic roles. Mg(2+) at low (<2 mM) concentration promoted UO(2)(2+)-specific activity, whereas Mg(2+) at high (>2 mM) concentration inhibited the UO(2)(2+)-specific activity. Therefore, the lock-and-key mode of DNAzymes depends on ionic strength, and the 39E DNAzyme is in the lock-and-key mode only at ionic strengths of 100 mM or greater.

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na(+) and Mg(2+)) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na(+) and Mg(2+) concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.

Atomistic analysis of pseudoknotted RNA unfolding

As important functional structures, RNA pseudoknots provide excellent models for studying the interplay between secondary and tertiary structures and the roles of triplexes, noncanonical interactions, and coaxial stacking in the folding/unfolding process. Here we report a first atomistic and statistical analysis of the unfolding of the pseudoknot within gene 32 mRNA of bacteriophage T2. Multiple unfolding pathways, diverse transition states, and various intermediate structures were observed. Water molecules were found to be coupled with the unfolding process via the expulsion or concurrent mechanism.

Predicting and modeling RNA architecture

A general approach for modeling the architecture of large and structured RNA molecules is described. The method exploits the modularity and the hierarchical folding of RNA architecture that is viewed as the assembly of preformed double-stranded helices defined by Watson-Crick base pairs and RNA modules maintained by non-Watson-Crick base pairs. Despite the extensive molecular neutrality observed in RNA structures, specificity in RNA folding is achieved through global constraints like lengths of helices, coaxiality of helical stacks, and structures adopted at the junctions of helices. The Assemble integrated suite of computer tools allows for sequence and structure analysis as well as interactive modeling by homology or ab initio assembly with possibilities for fitting within electronic density maps. The local key role of non-Watson-Crick pairs guides RNA architecture formation and offers metrics for assessing the accuracy of three-dimensional models in a more useful way than usual root mean square deviation (RMSD) values.

Predicting ion binding properties for RNA tertiary structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.

RNA folding in living cells

RNA folding is the most essential process underlying RNA function. While significant progress has been made in understanding the forces driving RNA folding in vitro, exploring the rules governing intracellular RNA structure formation is still in its infancy. The cellular environment hosts a great diversity of factors that potentially influence RNA folding in vivo. For example, the nature of transcription and translation is known to shape the folding landscape of RNA molecules. Trans-acting factors such as proteins, RNAs and metabolites, among others, are also able to modulate the structure and thus the fate of an RNA. Here we summarize the ongoing efforts to uncover how RNA folds in living cells.

Counterion condensation and shape within Poisson-Boltzmann theory

An analytical approximation to the nonlinear Poisson-Boltzmann (PB) equation is applied to charged macromolecules that possess one-dimensional symmetry and can be modeled by a plane, infinite cylinder, or sphere. A functional substitution allows the nonlinear PB equation subject to linear boundary conditions to be transformed into an approximate linear (Debye-Hückel-type) equation subject to nonlinear boundary conditions. A simple analytical result for the surface potential of such polyelectrolytes follows, leading to expressions for the amount of condensed (or renormalized) charge and the electrostatic Helmholtz energy for polyelectrolytes. Analytical high-charge/low-salt and low-charge/high-salt limits are shown to be similar to results obtained by others based on PB or counterion condensation theory. Several important general observations concerning polyelectrolytes treated within the context of PB theory can be made including: (1) all charged surfaces display some counterion condensation for finite electrolyte concentration, (2) the effect of surface geometry is described primarily by the sum of the Debye constant and the mean curvature of the surface, (3) two surfaces with the same surface charge density and mean curvature condense approximately identical fractions of counterions, (4) the amount of condensation is not determined by a predefined "condensation distance" although such a distance can be determined uniquely from it, and (5) substantial condensation occurs if the Debye constant of the electrolyte is much less than the mean curvature of a highly charged polyelectrolyte.

Quantifying the relationship between sequence and three-dimensional structure conservation in RNA

Background

In recent years, the number of available RNA structures has rapidly grown reflecting the increased interest on RNA biology. Similarly to the studies carried out two decades ago for proteins, which gave the fundamental grounds for developing comparative protein structure prediction methods, we are now able to quantify the relationship between sequence and structure conservation in RNA.

Results

Here we introduce an all-against-all sequence- and three-dimensional (3D) structure-based comparison of a representative set of RNA structures, which have allowed us to quantitatively confirm that: (i) there is a measurable relationship between sequence and structure conservation that weakens for alignments resulting in below 60% sequence identity, (ii) evolution tends to conserve more RNA structure than sequence, and (iii) there is a twilight zone for RNA homology detection.

Discussion

The computational analysis here presented quantitatively describes the relationship between sequence and structure for RNA molecules and defines a twilight zone region for detecting RNA homology. Our work could represent the theoretical basis and limitations for future developments in comparative RNA 3D structure prediction.

Predicting secondary structural folding kinetics for nucleic acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.

Dissecting electrostatic screening, specific ion binding, and ligand binding in an energetic model for glycine riboswitch folding

Riboswitches are gene-regulating RNAs that are usually found in the 5'-untranslated regions of messenger RNA. As the sugar-phosphate backbone of RNA is highly negatively charged, the folding and ligand-binding interactions of riboswitches are strongly dependent on the presence of cations. Using small angle X-ray scattering (SAXS) and hydroxyl radical footprinting, we examined the cation dependence of the different folding stages of the glycine-binding riboswitch from Vibrio cholerae. We found that the partial folding of the tandem aptamer of this riboswitch in the absence of glycine is supported by all tested mono- and divalent ions, suggesting that this transition is mediated by nonspecific electrostatic screening. Poisson-Boltzmann calculations using SAXS-derived low-resolution structural models allowed us to perform an energetic dissection of this process. The results showed that a model with a constant favorable contribution to folding that is opposed by an unfavorable electrostatic term that varies with ion concentration and valency provides a reasonable quantitative description of the observed folding behavior. Glycine binding, on the other hand, requires specific divalent ions binding based on the observation that Mg(2+), Ca(2+), and Mn(2+) facilitated glycine binding, whereas other divalent cations did not. The results provide a case study of how ion-dependent electrostatic relaxation, specific ion binding, and ligand binding can be coupled to shape the energetic landscape of a riboswitch and can begin to be quantitatively dissected.

Salt-dependent folding energy landscape of RNA three-way junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg(2+) ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na(+) and Mg(2+) ion concentrations. For Mg(2+) solutions, the TBI model, which accounts for the Mg(2+) ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg(2+) in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.

Extended structures in RNA folding intermediates are due to nonnative interactions rather than electrostatic repulsion

RNA folding occurs via a series of transitions between metastable intermediate states for Mg(2+) concentrations below those needed to fold the native structure. In general, these folding intermediates are considerably less compact than their respective native states. Our previous work demonstrates that the major equilibrium intermediate of the 154-residue specificity domain (S-domain) of the Bacillus subtilis RNase P RNA is more extended than its native structure. We now investigate two models with falsifiable predictions regarding the origins of the extended intermediate structures in the S-domains of the B. subtilis and the Escherichia coli RNase P RNA that belong to different classes of P RNA and have distinct native structures. The first model explores the contribution of electrostatic repulsion, while the second model probes specific interactions in the core of the folding intermediate. Using small-angle X-ray scattering and Langevin dynamics simulations, we show that electrostatics plays only a minor role, whereas specific interactions largely account for the extended nature of the intermediate. Structural contacts in the core, including a nonnative base pair, help to stabilize the intermediate conformation. We conclude that RNA folding intermediates adopt extended conformations due to short-range, nonnative interactions rather than generic electrostatic repulsion of helical domains. These principles apply to other ribozymes and riboswitches that undergo functionally relevant conformational changes.

Assembly mechanisms of RNA pseudoknots are determined by the stabilities of constituent secondary structures

Understanding how RNA molecules navigate their rugged folding landscapes holds the key to describing their roles in a variety of cellular functions. To dissect RNA folding at the molecular level, we performed simulations of three pseudoknots (MMTV and SRV-1 from viral genomes and the hTR pseudoknot from human telomerase) using coarse-grained models. The melting temperatures from the specific heat profiles are in good agreement with the available experimental data for MMTV and hTR. The equilibrium free energy profiles, which predict the structural transitions that occur at each melting temperature, are used to propose that the relative stabilities of the isolated helices control their folding mechanisms. Kinetic simulations, which corroborate the inferences drawn from the free energy profiles, show that MMTV folds by a hierarchical mechanism with parallel paths, i.e., formation of one of the helices nucleates the assembly of the rest of the structure. The SRV-1 pseudoknot, which folds in a highly cooperative manner, assembles in a single step in which the preformed helices coalesce nearly simultaneously to form the tertiary structure. Folding occurs by multiple pathways in the hTR pseudoknot, the isolated structural elements of which have similar stabilities. In one of the paths, tertiary interactions are established before the formation of the secondary structures. Our work shows that there are significant sequence-dependent variations in the folding landscapes of RNA molecules with similar fold. We also establish that assembly mechanisms can be predicted using the stabilities of the isolated secondary structures.